Chapter 13: Risk, Cost of Capital, and Capital Budgeting
13.1
The discount rate for the project is equal to the expected return for the security,
R
S
, since
the project has the same risk as the firm as a whole.
Apply the CAPM to express the
firm’s required return,
R
S
, in terms of the firm’s beta,
β
, the riskfree rate,
R
F
, and the
expected market return,
R
M
.
R
S
=
R
F
+
β
×
(
R
M
–
R
F
)
= 0.05 + 0.95 (0.09)
= 0.1355
Subtract the initial investment at year 0.
To calculate the PV of the cash inflows, apply
the annuity formula, discounted at 0.1355.
NPV
= C
0
+ C
1
A
T
r
= $1,200,000 + $340,000 A
5
0.1355
=
$20,016.52
Do not undertake the project since the NPV is negative.
13.2
a.
Calculate the average return for Douglas stock and the market.
R
D
= (Sum of Yearly Returns) / (Number of Years)
= (0.05 + 0.05 + 0.08 + 0.15 + 0.10) / (5)
=
0.066
R
M
= (0.12 + 0.01 + 0.06 + 0.10 + 0.05) / (5)
=
0.020
To calculate the beta of Douglas stock, calculate the variance of the market, (
R
M

R
M
)
2
, and the covariance of Douglas stock’s return with the market’s return, (
R
D

R
D
)
×
(
R
M

R
M
).
The beta of Douglas stock is equal to the covariance of
Douglas stock’s return and the market’s return divided by the variance of the
market.
Remember to divide both the covariance of Douglas stock’s return and
the market’s return and the variance of the market by 4.
Because the data are
historical, the appropriate denominator in the calculation of the variance is 4 (=
T
– 1).
R
D

R
D
R
M

R
M
(R
M

R
M
)
2
(R
D

R
D
) (R
M

R
M
)
0.116
0.14
0.0196
0.01624
0.016
0.01
0.0001
0.00016
0.014
0.04
0.0016
0.00056
0.084
0.08
0.0064
0.00672
0.034
0.03
0.0009
0.00102
0.0286
0.02470
β
D
= [Cov (
R
D
,
R
M
) / (T1)] / [Var (
R
M
) / (T1)]
= (0.02470 / 4) / (0.0286 / 4)
=
0.864
Answers to EndofChapter Problems
B186